A step towards the cluster positivity conjecture

Mathematics – Quantum Algebra

Scientific paper

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Comments welcome, v2:16 pages. introduction expanded. section 4 added in order to compare with the known formula when r=2. ref

Scientific paper

We prove a conjecture of Kontsevich, which asserts that the iterations of the
noncommutative rational map $F_r:(x,y)-->(xyx^{-1},(1+y^r)x^{-1})$ are given by
noncommutative Laurent polynomials with nonnegative integer coefficients.

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